where \(\frac{\delta E(\rho )}{\delta \rho (s)}\)  is the functional derivative with respect to \(\rho (s)\) . With the classical variational method, one can explicitly compute this derivative as follows (see [1]}):
\(\frac{\delta E(\rho )}{\delta \rho }(\theta ,t)=\mathbb {E}_{x\sim \mu }\left(p^\top _\rho (t;x)f(Z_\rho (t;x),\theta )\right)\,,\) 
